Mbappe is a world-class player who has made many achievements with his club, so it is natural for Real Madrid to bring in Mbappe. The reason is, Real Madrid is always able to bring in star players. Good examples include Ronaldo, Roberto Carlos, Kaka, Beckham, Eto'o, and many others. So in essence, the Real Madrid analysis team is very clever in selecting the players they bring in and apart from that, Real Madrid's finances are always stable. That's why Real Madrid is always able to bring in great and very expensive players like Mbappe.
Mbappe is currently unable to show his best performance. But sooner or later Mbappe will definitely be able to bring out all his best abilities for Real Madrid.
Because they are Real Madrid and they won the most UCL and UCL is the highest award in world of football, outside of World Cup for national games obviously, but for club purposes UCL is the best one. Think of it this way, any player who joins Real Madrid thinks they have a chance to win UCL title, and this means they will be more likely prefer them, whatever team looks the most successful one for them, they will go there.
Money of course plays a big role too, if Real offered him like 10 million a year or something obviously he wouldn't accept, but Real has money too and they offered a good chunk of money to him.
Players care about getting trophies, aside from money, that is the next thing they care about and Real offers these players a chance to win something big. Hopefully they will end up getting a title again but I can't see them winning it this year, Mbappe hasn't made improvements on the team, they have been just decent but not great like people expected.